Problem: Floyd is an aspiring music artist. He has a record contract that pays him a base rate of $\$200$ a month and an additional $\$12$ for each album that he sells. Last month he earned a total of $\$644$. Write an equation to determine the number of albums $(a)$ Floyd sold last month. Find the number of albums Floyd sold last month.
Solution: Let $a$ be the number of albums Floyd sold last month. Floyd earns $\$200$ in base pay each month. His earnings from $a$ album sales is $\$12a$. His total monthly earnings is $200+12a$. Since Floyd earned a total of $\$644$ last month, let's set this equal to $644$ : $ 200+12a=644$ Now, let's solve the equation to find the number of albums $(a)$ Floyd sold last month. $\begin{aligned} 200+12a&=644\\ \\ 200+12a{-200}&=644{-200}&&{\text{subtract }200} \text{ from each side}\\ \\ 12a&=444\\ \\ \dfrac{12a}{{12}}&=\dfrac{444}{{12}}&&\text{divide each side by ${12}$}\\ \\ \\ a&=37\end{aligned}$ The equation is $200+12a=644$. Floyd sold $37$ albums last month.